Perhaps you are looking for the system to help describe the action when the mechanics are too generic. I would suggest taking a look at Harnmaster 1st edition (I can't speak to the later editions) which has a detailed hit table for the various body parts (and alters for facing...like primarily left side/right side or higher or lower elevation), the crit table also differentiated edge/pierce/blunt. Granted it is for low fantasy/medieval fights, but with a little work, could be adapted to your liking for T2k. It may be enough just to have the table for where you are hitting to be more descriptive...uppper arm, elbow, lower arm, wrist, hand.etc.
spicing up the melee by homebrewing more detail/mechanics into melee by borrowing from other systems might help.
Regarding HTH unarmed damage 1 and crit 4. Keep in mind specialities: Brawler +1 to close combat, melee +1 knife/bayonet/club, and martial artist drops your crit threshold to 3. Roll 3 successes and you just did a HTH crit (roll 10 on the head and that is instant death). Brass knuckles gives +1 damage?? (or ninja climbing claws etc). Knife/bayonet with dam 2 crit 3 just needs two rolled successes to be a crit. Axe with 3 dam and 3 crit, just needs to hit.
"enemies are able to block", only if they saved their slow action.